FIG. 5 shows a schematic layout of an optical pick-up system. Light emitted by a semiconductor laser 1 is converted into a parallel beam by collimator 2. The light is then reflected by a folding mirror 3 and led to objective lens 4, which focuses the light onto an optical information-recording medium 5 for recording and reproducing information.
The field pattern of the light emitted by the semiconductor laser 1 is elliptical as shown in FIG. 7, where the major axis is perpendicular to the layer direction (face of junction). In other words, the light beam has its energy elliptically distributed in a cross-section of the beam. In case of a usual semiconductor laser for recording applications, the FWHM (full width at half maximum) is approximately 8.5 degrees in the layer direction and approximately 17 degrees in the direction perpendicular to the layer direction. In the direction perpendicular to the layer direction (face of junction), the outer of the light from the semiconductor laser 1 may not couple to the collimator lens 2 and is not converted into a parallel beam, thus resulting in loss of light into the optics. Further, the cross-section of the light converted into a parallel beam has an elliptical energy distribution. If the light is focused onto the surface of the optical information-recording medium 5 as an optical spot, the optical spot is also elliptical.
Accordingly, various techniques have been developed so far to shape the light emitted by semiconductor lasers, with an elliptical energy distribution into one with a substantially circular energy distribution.
FIG. 6 shows an optical system in which prisms are combined to shape light with an elliptical cross-section into one with a substantially circular cross-section. The optical system using prisms has the drawbacks that it is large in size, expensive and troublesome in assembling operation. Further, the system may produce additional aberrations. A parallel beam is necessary for the operation of the prisms and a large numerical aperture for the collimator is required.
Another technique has been developed, in which a folding mirror is used for beam shaping. For example, refer to Japanese unexamined patent publication No. 9-167375. In this case, the mirror for beam-shaping is arranged behind a collimator lens, so that a distance between the mirror for beam-shaping and the semiconductor laser is lager. Accordingly, a large numerical aperture for the collimator is required.
Still another technique has been developed, in which an aspherical lens having different focal lengths in two directions perpendicular to the optical axis, is used for beam-shaping. Japanese unexamined patent publications No. 6-274931 and No. 6-294940 disclose techniques in which a toroidal lens is used as the aspherical lens. Further, Japanese unexamined patent publications No. 2001-6202 and No. 2001-160234 disclose techniques in which a lens having an anamorphic surface, to be described below, is used. In any of the above-mentioned techniques, one surface or both surfaces of the collimator lens are made aspherical for a beam-shaping function.
A toroidal surface as a aspherical surface can be obtained by defining a profile by Equation (1) shown below and rotating the profile around the axis parallel to X axis and passing through the point on Z axis, distant by Ry from the origin. The shape is spherical in Y-Z plane and aspherical in X-Z plane.
                              Z          ⁡                      (            x            )                          =                                                            c                x                            ⁢                              x                2                                                    1              +                                                1                  -                                                            (                                              1                        +                        k                                            )                                        ⁢                                          c                      x                      2                                        ⁢                                          x                      2                                                                                                    +                                    ∑                              i                =                1                            m                        ⁢                                          A                i                            ⁢                              x                                  2                  ⁢                                                                          ⁢                  i                                            ⁢                                                          ⁢                              (                                  X                  ⁢                                      -                                    ⁢                  Z                  ⁢                                                                          ⁢                  plane                                )                                                                        Eq        .                                  ⁢                  (          1          )                    cx is the curvature of a curve in the X-Z plane and Ry is a radius of a curve (circle) in the Y-Z plane. The second and succeeding terms are correction terms representing a deviation from the surface represented by the first term.
An anamorphic surface can be represented by Equation (2) shown below.
                    Z        =                                                                              c                  x                                ⁢                                  x                  2                                            +                                                c                  y                                ⁢                                  y                  2                                                                    1              +                                                1                  -                                                            (                                              1                        +                                                  k                          x                                                                    )                                        ⁢                                          (                                                                        c                          x                          2                                                ⁢                                                  x                          2                                                                    )                                                        -                                                            (                                              1                        +                                                  k                          y                                                                    )                                        ⁢                                          (                                                                        c                          y                          2                                                ⁢                                                  y                          2                                                                    )                                                                                                    +                                    AR              ⁡                              [                                                                            (                                              1                        -                        AP                                            )                                        ⁢                                          x                      2                                                        +                                                            (                                              1                        +                        AP                                            )                                        ⁢                                          y                      2                                                                      ]                                      2                    +                                    BR              ⁡                              [                                                                            (                                              1                        -                        Bp                                            )                                        ⁢                                          x                      2                                                        +                                                            (                                              1                        +                        BP                                            )                                        ⁢                                          y                      2                                                                      ]                                      3                    +                                    CR              ⁡                              [                                                                            (                                              1                        -                        CP                                            )                                        ⁢                                          x                      2                                                        +                                                            (                                              1                        +                        CP                                            )                                        ⁢                                          y                      2                                                                      ]                                      4                    +                                    DR              ⁡                              [                                                                            (                                              1                        -                        DP                                            )                                        ⁢                                          x                      2                                                        +                                                            (                                              1                        +                        DP                                            )                                        ⁢                                          y                      2                                                                      ]                                      5                                              Eq        .                                  ⁢                  (          2          )                    where cx is the curvature of a curve in the X-Z plane and equals 1/Rx and cy is curvature of a curve in the Y-Z plane and equals 1/Ry. The second and succeeding terms are correction terms representing a deviation from the surface represented by the first term. AR, BR, CR, DR, AP, BP, CP and DP are correction coefficients (constants).
In an optical pick-up system in compact discs (CD), digital versatile discs (DVD) or the like, the aberrations must be minimized for accurate and high-speed recording and reproducing. Accordingly, the aberrations for the above-mentioned lenses having a beam-shaping function must also be minimized.
Further, in optical communication systems using semiconductor lasers, a similar beam-shaping element is required for efficiently coupling beams emitted by a semiconductor laser to an optical fiber, for example, described in Japanese laying-open of unexamined application (KOKAI) No. 11-218649.
However, conventional beam-shaping optical elements using the above-mentioned equations (1) and (2) for the aspherical surfaces do not always lead to satisfactory results for minimization of aberrations.
Accordingly, there is a need to use a different description of the lens surface in order to minimize the aberrations of a beam-shaping optical element using an aspherical surface.